Reference problem
=====================


Geometry
---------


.. image:: images/10000000000004560000017749F3A2EF98E3C48C.png
    :width: 6.3374in
    :height: 2.0661in


.. _RefImage_10000000000004560000017749F3A2EF98E3C48C.png:

The system represented in the diagram above is composed of two coaxial cylinders and a fluid flowing at the speed u in the annular space between the two cylinders. The dimensions are:


* inner radius: :math:`{R}_{i}=1m`;


* outer radius: :math:`{R}_{e}=1.05m`;


* length: :math:`L=100m`.


Material properties
------------------------

**Structure:**

Young's modulus: :math:`E\mathrm{=}{2.10}^{11}\mathit{Pa}`;

Poisson's ratio: :math:`\nu =0.3`;

density: :math:`{\rho }_{s}=7800\mathrm{kg}/{m}^{3}`.

**Fluid:**

density: :math:`\rho =1000\mathrm{kg}/{m}^{3}`.


Boundary conditions and loads
-------------------------------------

**Structure:**

blocking the nodes of the inner cylinder;

ball joint at points :math:`A` and :math:`B` of the external cylinder.

**Fluid:**

different speeds are imposed at the entrance to the fluid domain with normal heat fluxes equal to :math:`4m/s`, :math:`0.5m/s`, :math:`1.5m/s`, :math:`2m/s`, :math:`2.2m/s` and :math:`2.688m\mathrm{/}s` (critical speed).


Initial conditions
--------------------

Not applicable.